Pressure at the walls of a container

  • Thread starter Kaguro
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  • #1
Kaguro
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Homework Statement:
Consider a cube ABCDEFGH of volume V containing N molecules each of mass m with
uniform density n =N/V . Suppose this system is equivalent to a system of M non-interacting gases such that molecules of the i th gas are N_i = n_i*V in number, each with an
identical y -component of velocity v_i . What is the pressure P on the surface , ABCD of
area A, perpendicular to the positive y axis?
Relevant Equations:
PV=NkT, where N is total number of molecules
Vrms=sqrt(1.5kT)
I wrote energy of each molecule is ##\frac{1}{2}mv_{rms}^2 \Rightarrow E/3 = \frac{1}{2}mv_i^2##. So total energy of each type of gas is
##E_i = N_i\frac{3}{2}mv_i^2## Now, PV=E. So total Pressure = Sum of energies/volume
##P=\frac{\frac{3m}{2}\sum_i N_i v_i^2}{V} =\frac{3m}{2} \sum_i n_i v_i^2 ##

But answer given is just ##m \sum_i n_i v_i^2 ##
Help.
 

Answers and Replies

  • #2
mjc123
Science Advisor
Homework Helper
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You are not told anything about the x and z components of the velocity. You cannot assume that they are the same as the y component, or that the pressure is isotropic, so you can't use PV = E.
Incidentally, there is presumably a mistake in the question; at any instant half the molecules have y-velocity vi, and the other half -vi.
 

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